A Study On Two Classes Of Risk Processes

With the development of the financial market, risk theory is also getting better, one of the main issues is embodied in bankruptcy. It is mainly discussing about ruin probability, survival probability, the surplus immediately before ruin and deficit at ruin within the limited time. In recent years, many scholars have promoted the classical risk model, and then studied the bankruptcy problem from different angles.The classical risk model is a more utopian model, so it has great limitations in actual life. Therefore, to the promotion of the classical risk model, making it more practical value has become the mainstream of the risk. Such as:more and more scholars pay attention to the two classes of claims. This model is proposed mainly by Li in the literature [2], the main consideration of two classes of claims, the number of the first kind of claims is a Poisson process, another is a Erlang (2) process. Based on this risk model, we get a new model.The innovations mainly have the following aspects:First, Based on the model that the claim of number are subject to Poisson distribution and Erlang(2) distribution, we discuss the dual risk model, the main research is to meet some Integro-differential equations of the survival probability and related results.Second, we have considered two classes of claims happen times are subject to the distribution of Erlang (2) base on the risk model in the literature [3]. The Gerber-Shiu penalty function which meet the integral differential equations and some related boundary conditions are obtained in this paper.Third, we consider barrier dividend strategy on the basis of the model which studies two classes of claims in this paper, the Gerber-Shiu penalty function, the sum of the dividend moments generating function that meet the integral differential equations and some related boundary conditions are given, respectively.